When I type a shortcut for a snippet e.g. ssf (very known shortcut) I get also the description of the snippet.

But unfortunately the description disappears from the dialog which appears when you type a shortcut since the last version(s).
The columns it's remove in general from the tooltip dialog?
I have to configure my SQL Prompt correctly?

Do you mean where it says "SELECT * FROM fragment" in grey on the right of the suggestions box? I still see this text on my machine with SQL Prompt 5.3.2.2.

If the object definition box is missing (the extra box that flies out with the full expansion of the snippet) then ensure that "Display object definitions" in SQL Prompt 5 > Options... > Behavior is checked.

I tried the mentioned method to uninstall and downgrade to the old version 5.3.0.3. But unfortunately the problem is not solved.
Any other ideas? I could also try to delete/rename my local SQL Prompt 5 configuration folder and install SQL Prompt afterwards again.

I'm using the SSMS 2008 Build 10.0.5500.0. Do you need any other information?

That's very strange. Maybe one of the SQL Prompt local configuration files has got something wrong in it, so renaming the %LocalAppData%\\Red Gate\\SQL Prompt 5 out of the way could be worth a try. You won't need to reinstall SQL Prompt.

In that directory, RedGate_SQLPrompt_CommonUI_Options_UIOptions.xml has an entry <CandidateListColumnDivider>, which controls how far across the grey text should start. Although the user interface shouldn't let you move the grey text completely out of the way, if something has caused this value to be outside the range of 0.125 to 0.875 then the grey text could disappear. For instance, I manually edited the value to 1.0 and couldn't see the grey text at all.

Renaming the directory as above will reset SQL Prompt's settings, but you could also take a look inside that XML file to see if there is an odd value there.